Quantum Groups

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pp: 1–38

DOI: 10.4171/047-1/1

Lectures on tensor categories

Damien Calaque[1] and Pavel Etingof[2]

(1) I3M, Université Montpellier 2, Case courrier 051, 34095, Montpellier CEDEX 5, France
(2) Department of Mathematics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, MA 02139-4307, Cambridge, USA

We give a review of some recent developments in the theory of tensor categories. The topics include realizability of fusion rings, Ocneanu rigidity, module categories, weak Hopf algebras, Morita theory for tensor categories, lifting theory, categorical dimensions, Frobenius–Perron dimensions, and classification of tensor categories.

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